Identify and extend the pattern to find the next number in this sequence: 2, 8, 32, 128, a. 152 b. 134 c. 224 d. 512

Given that the sequence is:
2, 8, 32, 128, ...
The series is a geometric sequence because there is a common ratio between the consecutive numbers. Thus it will follow the explicit form given by:
an=ar^(n-1)
where:
a=first term
r= common ratio
n= nth term
from the sequence:
a=2
r=8/2=4
thus the explicit formula for the sequence is:
an=2(4^(n-1))
thus the next term which is the fifth term will be:
a5=2(4^(5-1))
a5=512

D